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arXiv · 2402.03586

Error estimates for SUPG-stabilised Dynamical Low Rank Approximations

Fabio Nobile·Thomas Trigo Trindade
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Abstract

We perform an error analysis of a fully discretised Streamline Upwind Petrov Galerkin Dynamical Low Rank (SUPG-DLR) method for random time-dependent advection-dominated problems. The time integration scheme has a splitting-like nature, allowing for potentially efficient computations of the factors characterising the discretised random field. The method allows to efficiently compute a low-rank approximation of the true solution, while naturally "inbuilding" the SUPG stabilisation. Standard error rates in the L2 and SUPG-norms are recovered. Numerical experiments validate the predicted rates.

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Fabio Nobile, Thomas Trigo Trindade. 2024-02-05. Error estimates for SUPG-stabilised Dynamical Low Rank Approximations. https://arxiv.org/abs/2402.03586

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